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Atom Diffusion Controls Dynamics of Surface Phase Transition on Si (111)
by J. B. Hannon, N. C. Bartelt, B. S. Swartzentruber, and G. L. Kellogg

MotivationMaterials that undergo phase transitions can dramatically change their properties as a result of small external inputs.  Understanding the dynamics of phase transitions is an important step in the quest to understand complex collective behavior.  In many systems, phase transitions require the transport of atoms from one phase to the other due to differences in atomic density.  In these cases, the kinetics of mass transport can be just as important as the thermodynamic differences between the two phases in defining the rate of the transformation.  Although such diffusion processes can be treated theoretically, they are difficult to address experimentally.  By studying phase transitions on a surface, we are able to quantify the mass transport process and assess its importance in controlling the dynamics of the transition.

Accomplishment We have used low-energy electron microscopy (LEEM) to show that adatom diffusion controls the dynamics of the phase transition between the 7x7 and 1x1 surface structures on Si(111). The equilibrium structure of the Si(111) surface at room temperature is a complicated reconstruction with 7x7 periodicity.  At a temperature of 820 C this surface undergoes a first-order phase transition to a structure that gives a 1x1 diffraction pattern.  This high-temperature 1x1 phase is a dense overlayer of adatoms (6% more dense than 7x7) residing on the bulk-terminated structure. To study the dynamics of the transition, we made real-time observations of the time evolution of triangular 7x7 domains during growth of the 1x1 phase.  Figure 1 shows a series of LEEM images taken as the surface transforms from the 7x7 to 1x1 structure.  The bright areas correspond to the 7x7 domains.  Figure 2 shows a plot of the area of several domains as a function of time. We find that the domains decay approximately linearly in time with a decay rate determined, not by the domain size, but by the local arrangement of neighboring domains.  This observation is counter to the simplest picture of phase boundary motion, in which domain walls move with a constant velocity (independent of environment) determined by the free energy difference between the two phases. We have modeled the effect of this mass transport requirement on the observed decay by solving the two-dimensional diffusion equation for the experimentally observed configuration of 7x7 domains.  From this analysis, we find that the decay is limited by the supply of additional material to the boundary. Moreover, the analysis is consistent with a model in which sources of adatoms are uniformly distributed on the surface. The model reproduces the simultaneous decay of all islands in the field of view with only one adjustable parameter (Fig. 2).  The results lead us to conclude that random adatom-vacancy generation provides the source of material required for the transition to proceed.

SignificanceThis work identifies an important aspect of phase transitions that is difficult to address experimentally and therefore often overlooked. We were able to quantify the role of mass transport in surface phase transitions by observing the phase transformation as it occurs. In the process, we discovered a novel precipitation mechanism involving the random creation of adatom and vacancies at the surface and subsequent diffusion of the adatoms to the domain boundaries.

Figure 1.  Low energy electron microscope images showing the decay of 7x7 domains during the 7x7 to 1x1 phase transition on Si(111). The field of view is 2.5 microns and the temperature is 830 C. Figure 2. Decay rates for selected 7x7 domains.  The LEEM image has a field of view of 2.5 microns.  Dots are measured rates from LEEM images.  Blue lines are fits from a diffusion equation model with one adjustable parameter.
J. B. Hannon, H. Hibino, N. C. Bartelt, B. S. Swartzentruber, T. Ogino, and G. L. Kellogg, Nature 405, 552 (2000).
Work supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering
Last modified December 29, 2003
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